Solve using the Square Root Property 125=2x*x

Math
125=2x⋅x
Rewrite the equation as 2x⋅x=125.
2x⋅x=125
Simplify.
Tap for more steps…
Raise x to the power of 1.
2(x1x)=125
Raise x to the power of 1.
2(x1x1)=125
Use the power rule aman=am+n to combine exponents.
2×1+1=125
Add 1 and 1.
2×2=125
2×2=125
Divide each term by 2 and simplify.
Tap for more steps…
Divide each term in 2×2=125 by 2.
2×22=1252
Cancel the common factor of 2.
Tap for more steps…
Cancel the common factor.
2×22=1252
Divide x2 by 1.
x2=1252
x2=1252
x2=1252
Take the square root of both sides of the equation to eliminate the exponent on the left side.
x=±1252
The complete solution is the result of both the positive and negative portions of the solution.
Tap for more steps…
Simplify the right side of the equation.
Tap for more steps…
Rewrite 1252 as 1252.
x=±1252
Simplify the numerator.
Tap for more steps…
Rewrite 125 as 52⋅5.
Tap for more steps…
Factor 25 out of 125.
x=±25(5)2
Rewrite 25 as 52.
x=±52⋅52
x=±52⋅52
Pull terms out from under the radical.
x=±552
x=±552
Multiply 552 by 22.
x=±552⋅22
Combine and simplify the denominator.
Tap for more steps…
Multiply 552 and 22.
x=±55222
Raise 2 to the power of 1.
x=±55222
Raise 2 to the power of 1.
x=±55222
Use the power rule aman=am+n to combine exponents.
x=±55221+1
Add 1 and 1.
x=±55222
Rewrite 22 as 2.
Tap for more steps…
Use axn=axn to rewrite 2 as 212.
x=±552(212)2
Apply the power rule and multiply exponents, (am)n=amn.
x=±552212⋅2
Combine 12 and 2.
x=±552222
Cancel the common factor of 2.
Tap for more steps…
Cancel the common factor.
x=±552222
Divide 1 by 1.
x=±5522
x=±5522
Evaluate the exponent.
x=±5522
x=±5522
x=±5522
Simplify the numerator.
Tap for more steps…
Combine using the product rule for radicals.
x=±52⋅52
Multiply 2 by 5.
x=±5102
x=±5102
x=±5102
The complete solution is the result of both the positive and negative portions of the solution.
Tap for more steps…
First, use the positive value of the ± to find the first solution.
x=5102
Next, use the negative value of the ± to find the second solution.
x=-5102
The complete solution is the result of both the positive and negative portions of the solution.
x=5102,-5102
x=5102,-5102
x=5102,-5102
The result can be shown in multiple forms.
Exact Form:
x=5102,-5102
Decimal Form:
x=7.90569415…,-7.90569415…
Solve using the Square Root Property 125=2x*x

Download our
App from the store

Create a High Performed UI/UX Design from a Silicon Valley.

Scroll to top